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90
Adaptive submodularity: Theory and applications in active learning and stochastic optimization
 J. Artificial Intelligence Research
, 2011
"... Many problems in artificial intelligence require adaptively making a sequence of decisions with uncertain outcomes under partial observability. Solving such stochastic optimization problems is a fundamental but notoriously difficult challenge. In this paper, we introduce the concept of adaptive subm ..."
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Cited by 70 (15 self)
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Many problems in artificial intelligence require adaptively making a sequence of decisions with uncertain outcomes under partial observability. Solving such stochastic optimization problems is a fundamental but notoriously difficult challenge. In this paper, we introduce the concept of adaptive submodularity, generalizing submodular set functions to adaptive policies. We prove that if a problem satisfies this property, a simple adaptive greedy algorithm is guaranteed to be competitive with the optimal policy. In addition to providing performance guarantees for both stochastic maximization and coverage, adaptive submodularity can be exploited to drastically speed up the greedy algorithm by using lazy evaluations. We illustrate the usefulness of the concept by giving several examples of adaptive submodular objectives arising in diverse AI applications including management of sensing resources, viral marketing and active learning. Proving adaptive submodularity for these problems allows us to recover existing results in these applications as special cases, improve approximation guarantees and handle natural generalizations. 1.
Toward community sensing.
 In ACM/IEEE International Conference on Information Processing in Sensor Networks (IPSN),
, 2008
"... Abstract A great opportunity exists to fuse information from populations of privatelyheld sensors to create useful sensing applications. For example, GPS devices, embedded in cellphones and automobiles, might one day be employed as distributed networks of velocity sensors for traffic monitoring an ..."
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Cited by 65 (8 self)
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Abstract A great opportunity exists to fuse information from populations of privatelyheld sensors to create useful sensing applications. For example, GPS devices, embedded in cellphones and automobiles, might one day be employed as distributed networks of velocity sensors for traffic monitoring and routing. Unfortunately, privacy and resource considerations limit access to such data streams. We describe principles of community sensing that offer mechanisms for sharing data from privately held sensors. The methods take into account the likely availability of sensors, the contextsensitive value of sensor information, based on models of phenomena and demand, and sensor owners' preferences about privacy and resource usage. We present efficient and wellcharacterized approximations of optimal sensing policies. We provide details on key principles of community sensing and highlight their use within a case study for road traffic monitoring.
Efficient Informative Sensing using Multiple Robots
"... The need for efficient monitoring of spatiotemporal dynamics in large environmental applications, such as the water quality monitoring in rivers and lakes, motivates the use of robotic sensors in order to achieve sufficient spatial coverage. Typically, these robots have bounded resources, such as l ..."
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Cited by 56 (5 self)
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The need for efficient monitoring of spatiotemporal dynamics in large environmental applications, such as the water quality monitoring in rivers and lakes, motivates the use of robotic sensors in order to achieve sufficient spatial coverage. Typically, these robots have bounded resources, such as limited battery or limited amounts of time to obtain measurements. Thus, careful coordination of their paths is required in order to maximize the amount of information collected, while respecting the resource constraints. In this paper, we present an efficient approach for nearoptimally solving the NPhard optimization problem of planning such informative paths. In particular, we first develop eSIP (efficient Singlerobot Informative Path planning), an approximation algorithm for optimizing the path of a single robot. Hereby, we use a Gaussian Process to model the underlying phenomenon, and use the mutual information between the visited locations and remainder of the space to quantify the amount of information collected. We prove that the mutual information collected using paths obtained by using eSIP is close to the information obtained by an optimal solution. We then provide a general technique, sequential allocation, which can be used to extend any single robot planning algorithm, such as eSIP, for the multirobot problem. This procedure approximately generalizes any guarantees for the singlerobot problem to the multirobot case. We extensively evaluate the effectiveness of our approach on several experiments performed infield for two important environmental sensing applications, lake and river monitoring, and simulation experiments performed using several real world sensor network data sets. 1.
Privately releasing conjunctions and the statistical query barrier
 In STOC
, 2011
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Adaptive Submodularity: A New Approach to Active Learning and Stochastic Optimization
"... Solving stochastic optimization problems under partial observability, where one needs to adaptively make decisions with uncertain outcomes, is a fundamental but notoriously difficult challenge. In this paper, we introduce the concept of adaptive submodularity, generalizing submodular set functions t ..."
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Cited by 40 (3 self)
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Solving stochastic optimization problems under partial observability, where one needs to adaptively make decisions with uncertain outcomes, is a fundamental but notoriously difficult challenge. In this paper, we introduce the concept of adaptive submodularity, generalizing submodular set functions to adaptive policies. We prove that if a problem satisfies this property, a simple adaptive greedy algorithm is guaranteed to be competitive with the optimal policy. We illustrate the usefulness of the concept by giving several examples of adaptive submodular objectives arising in diverse applications including sensor placement, viral marketing and poolbased active learning. Proving adaptive submodularity for these problems allows us to recover existing results in these applications as special cases and leads to natural generalizations. 1
Bounded approximate decentralised coordination using the maxsum algorithm
 IN DISTRIBUTED CONSTRAINT REASONING WORKSHOP
, 2009
"... In this paper we propose a novel algorithm that provides bounded approximate solutions for decentralised coordination problems. Our approach removes cycles in any general constraint network by eliminating dependencies between functions and variables which have the least impact on the solution qualit ..."
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Cited by 30 (9 self)
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In this paper we propose a novel algorithm that provides bounded approximate solutions for decentralised coordination problems. Our approach removes cycles in any general constraint network by eliminating dependencies between functions and variables which have the least impact on the solution quality. It uses the maxsum algorithm to optimally solve the resulting tree structured constraint network, providing a bounded approximation specific to the particular problem instance. We formally prove that our algorithm provides a bounded approximation of the original problem and we present an empirical evaluation in a synthetic scenario. This shows that the approximate solutions that our algorithm provides are typically within 95 % of the optimum and the approximation ratio that our algorithm provides is typically 1.23.
Efficient multirobot search for a moving target
 Int. J. Robotics Research
, 2009
"... This paper examines the problem of locating a mobile, nonadversarial target in an indoor environment using multiple robotic searchers. One way to formulate this problem is to assume a known environment and choose searcher paths most likely to intersect with the path taken by the target. We refer to ..."
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Cited by 29 (14 self)
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This paper examines the problem of locating a mobile, nonadversarial target in an indoor environment using multiple robotic searchers. One way to formulate this problem is to assume a known environment and choose searcher paths most likely to intersect with the path taken by the target. We refer to this as the multirobot efficient search path planning (MESPP) problem. Such path planning problems are NPhard, and optimal solutions typically scale exponentially in the number of searchers. We present an approximation algorithm that utilizes finitehorizon planning and implicit coordination to achieve linear scalability in the number of searchers. We prove that solving the MESPP problem requires maximizing a nondecreasing, submodular objective function, which leads to theoretical bounds on the performance of our approximation algorithm. We extend our analysis by considering the scenario where searchers are given noisy nonlineofsight ranging measurements to the target. For this scenario, we derive and integrate online Bayesian measurement updating into our framework. We demonstrate the performance of our framework in two largescale simulated environments, and we further validate our results using data from a novel ultrawideband ranging sensor. Finally, we provide an analysis that demonstrates the rela
On the Vulnerability of Large Graphs
"... Given a large graph, like a computer network, which k nodes should we immunize (or monitor, or remove), to make it as robust as possible against a computer virus attack? We need (a) a measure of the ‘Vulnerability ’ of a given network, (b) a measure of the ‘Shieldvalue ’ of a specific set of k node ..."
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Cited by 26 (11 self)
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Given a large graph, like a computer network, which k nodes should we immunize (or monitor, or remove), to make it as robust as possible against a computer virus attack? We need (a) a measure of the ‘Vulnerability ’ of a given network, (b) a measure of the ‘Shieldvalue ’ of a specific set of k nodes and (c) a fast algorithm to choose the best such k nodes. We answer all these three questions: we give the justification behind our choices, we show that they agree with intuition as well as recent results in immunology. Moreover, we propose NetShield, a fast and scalable algorithm. Finally, we give experiments on large real graphs, where NetShield achieves tremendous speed savings exceeding 7 orders of magnitude, against straightforward competitors. 1
Distributed Welfare Games
"... We consider a variation of the resource allocation problem. In the traditional problem, there is a global planner who would like to assign a set of players to a set of resources so as to maximize welfare. We consider the situation where the global planner does not have the authority to assign player ..."
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Cited by 20 (7 self)
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We consider a variation of the resource allocation problem. In the traditional problem, there is a global planner who would like to assign a set of players to a set of resources so as to maximize welfare. We consider the situation where the global planner does not have the authority to assign players to resources; rather, players are selfinterested. The question that emerges is how can the global planner entice the players to settle on a desirable allocation with respect to the global welfare? To study this question, we focus on a class of games that we refer to as distributed welfare games. Within this context, we investigate how the global planner should distribute the welfare to the players. We measure the efficacy of a distribution rule in two ways: (i) Does a pure Nash equilibrium exist? (ii) How does the welfare associated with a pure Nash equilibrium compare to the global welfare associated with the optimal allocation? In this paper we explore the applicability of cost sharing methodologies for distributing welfare in such resource allocation problems. We demonstrate that obtaining desirable distribution rules, such as distribution rules that are budget balanced and guarantee the existence of a pure Nash equilibrium, often comes at a significant informational and computational cost. In light of this, we derive a systematic procedure for designing desirable distribution rules with a minimal informational and computational cost for a special class of distributed welfare games. Furthermore, we derive a bound on the price of anarchy for distributed welfare games in a variety of settings. Lastly, we highlight the implications of these results using the problem of sensor coverage.
Proofs and Experiments in Scalable, NearOptimal Search by Multiple Robots
"... Abstract — In this paper, we examine the problem of locating a nonadversarial target using multiple robotic searchers. This problem is relevant to many applications in robotics including emergency response and aerial surveillance. Assuming a known environment, this problem becomes one of choosing s ..."
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Cited by 19 (5 self)
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Abstract — In this paper, we examine the problem of locating a nonadversarial target using multiple robotic searchers. This problem is relevant to many applications in robotics including emergency response and aerial surveillance. Assuming a known environment, this problem becomes one of choosing searcher paths that are most likely to intersect with the path taken by the target. We refer to this as the Multirobot Efficient Search Path Planning (MESPP) problem. Such path planning problems are NPhard, and optimal solutions typically scale exponentially in the number of searchers. We present a finitehorizon path enumeration algorithm for solving the MESPP problem that utilizes sequential allocation to achieve linear scalability in the number of searchers. We show that solving the MESPP problem requires the maximization of a nondecreasing, submodular objective function, which directly leads to theoretical guarantees on paths generated by sequential allocation. We also demonstrate how our algorithm can run online to incorporate noisy measurements of the target’s position during search. We verify the performance of our algorithm both in simulation and in experiments with a novel radio sensor capable of providing range through walls. Our results show that our linearly scalable MESPP algorithm generates searcher paths competitive with those generated by exponential algorithms. I.